Highest Common Factor of 3575, 6730 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 3575, 6730 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 3575, 6730 is 5 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 3575, 6730 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 3575, 6730 is 5.
HCF(3575, 6730) = 5
HCF of 3575, 6730 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3575, 6730 is 5.
Highest Common Factor of 3575,6730 is 5
Step 1: Since 6730 > 3575, we apply the division lemma to 6730 and 3575, to get
6730 = 3575 x 1 + 3155
Step 2: Since the reminder 3575 ≠ 0, we apply division lemma to 3155 and 3575, to get
3575 = 3155 x 1 + 420
Step 3: We consider the new divisor 3155 and the new remainder 420, and apply the division lemma to get
3155 = 420 x 7 + 215
We consider the new divisor 420 and the new remainder 215,and apply the division lemma to get
420 = 215 x 1 + 205
We consider the new divisor 215 and the new remainder 205,and apply the division lemma to get
215 = 205 x 1 + 10
We consider the new divisor 205 and the new remainder 10,and apply the division lemma to get
205 = 10 x 20 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 3575 and 6730 is 5
Notice that 5 = HCF(10,5) = HCF(205,10) = HCF(215,205) = HCF(420,215) = HCF(3155,420) = HCF(3575,3155) = HCF(6730,3575) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 3575, 6730 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 3575, 6730?
Answer: HCF of 3575, 6730 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3575, 6730 using Euclid's Algorithm?
Answer: For arbitrary numbers 3575, 6730 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.